In a large bowl, mix ‚ cup salt, the sugar, and 6 cups water, stirring to dissolve the salt and sugar. Submerge the chicken, cover, and refrigerate for 1 hour. Rinse the chicken under running water and dry well. Lay a breast on a work surface, with the thick end toward you. Using a knife with a long, thin blade, cut a pocket about 2 inches wide and 3 inches deep into the thick end. Take care not to cut through the top, bottom, sides, or thin end. Repeat with the remaining breasts.

Meanwhile, in a small skillet over medium heat, heat 2 teaspoons oil until shimmering. Add the shallot and ¼ teaspoon salt, and cook, stirring, until softened, about 1½ minutes. Add the garlic and half the parsley and cook, stirring, until fragrant, about 30 seconds; cool the mixture completely.

With the rack in the center position, heat the oven to 400 degrees. Add 2 teaspoons oil to a shallow dish such as a pie plate. Lay the ham slices on a work surface and place 1 piece of cream cheese, 1 tablespoon chutney, and a quarter of the shallot mixture in the center of each slice. Roll up the ham slices, folding so no filling is exposed, into a rough tube shape. Holding each tube to keep it closed, roll it in oil and work it into the pocket in the chicken breast; fasten the open end with 1 or 2 toothpicks. Sprinkle the filled chicken breasts with pepper.

In a large ovenproof skillet over medium-high heat, heat the remaining 2 teaspoons oil until shimmering. Add the chicken and cook, undisturbed, until bottom is browned, about 3 minutes; turn and cook until the second side is browned, about 3 minutes longer. Transfer the skillet to the oven and roast until chicken (the meat, not the stuffing) registers 160 degrees on an instant-read thermometer, 12 to 18 minutes. Remove the chicken to a platter, tent loosely with foil, and set aside.

Taking great care with the scorching-hot skillet, place it over medium-high heat, add the vermouth and bring to a strong simmer; with a wooden spoon, scrape bottom of pan to loosen and dissolve the fond, about 15 seconds. Simmer vigorously, stirring, until liquid is reduced by about a third, about 1½ minutes. Add any accumulated chicken juices and the remaining 3 tablespoons chutney and cook, stirring, about 40 seconds longer. Adjust the heat to low, add the lemon juice and butter, and stir to incorporate it into the sauce. Taste and adjust the seasoning with pepper to taste. Add half of the remaining parsley and stir to mix. Pour the sauce over the chicken, sprinkle with the remaining parsley, and serve at once.

Jim Scherer for the boston globe

TIP: With the thin, pointed end facing away from you, cut a pocket into the thick end of the breast.

Variations

GORGONZOLA AND FIG-STUFFED CHICKEN BREASTS

Follow the directions for the Cream Cheese and Chutney-Stuffed Chicken Breasts, making the following changes:

1) In a small bowl, mix 2 finely chopped large dried figs (about 3 tablespoons chopped) and 2 teaspoons amontillado sherry and set aside, stirring occasionally, until figs absorb most of the liquid, about 20 minutes.

2) Along with the garlic, add 1½ teaspoons chopped fresh rosemary and the moistened figs to the shallot mixture.

3) For the filling, substitute Gorgonzola for the cream cheese and omit the chutney.

4) In the sauce, substitute amontillado sherry for the vermouth and 2 teaspoons honey for the chutney.

RED PEPPER AND OLIVE-STUFFED CHICKEN BREASTS

Follow the directions for the Cream Cheese and Chutney-Stuffed Chicken Breasts, making the following changes:

1) Substitute 3 tablespoons very finely chopped red bell pepper for the shallot, increase the quantity of garlic to 3 cloves, and along with the garlic add 3 tablespoons finely chopped pitted green olives to the red pepper mixture. Substitute chopped fresh basil for the parsley, adding 3 tablespoons of it to the filling and 1 tablespoon to the sauce.

2) Omit the chutney in the filling.

3) For the sauce, use dry white wine in place of vermouth and 2 teaspoons honey for the chutney, and reduce the lemon juice to ½ teaspoon.